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Earn 100
If , , and are in AP, then the GM of and is _____.
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Important Questions on Progressions
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Each of the series and is continued up to terms. Find how many terms are identical between the two series.
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Find the sum of the series till the rd term for the series: .
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What is the maximum sum of the terms in the arithmetic progression
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The th term of an AP is the geometric mean of the st and the nd terms of the same AP. Find the common difference of the AP, given that the sum of the first twenty-two terms of the AP is .
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How many terms of the series amount to ?
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Tom and Jerry were playing mathematical puzzles with each other. Jerry drew a square of side , and then kept on drawing squares inside the square by joining the mid-points of the squares. He continued this process indefinitely. Jerry asked Tom to determine the sum of the areas of all the squares that he drew. If Tom answered correctly, then what would be his answer?
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The sum of the first two terms of an infinite geometric series is . Also, each term of the series is equal to the sum of all the terms that follow. Find the sum of the series.
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An equilateral triangle is drawn by joining the mid-points of the sides of another equilateral triangle. Another equilateral triangle is drawn inside the previous one, joining the mid-points of the sides of the previous equilateral triangle, and the process continues infinitely. Find the sum of the areas of all the equilateral triangles, if the side of the largest equilateral triangle is units.
